This page lists some of the differences between the latest versions of the major browsers that are relevant to Emscripten-compiled applications and games:
emscripten_get_now() returns a wallclock time as a
float in milliseconds. Opera 12.16 and Windows Google Chrome 28.0.1500.95 have a limitation that the timer precision is only in milliseconds. On other major browsers (IE10, Firefox 22, Chrome 28 on non-Windows) it has sub-millisecond precision.
WebGL is not fully supported on Internet Explorer (at least prior to IE12):
Internet Explorer 10 and older do not support WebGL. Trying to initialize a GL context via EGL, GLUT, SDL or similar will fail. Emscripten applications that do not depend on OpenGL can still run on this browser.
Internet Explorer 11 supports only part of WebGL 1.0. Some commands, shaders etc. may not work. You may be able to limit your app to using the subset that is supported by IE11.
WebGL support on other major browsers is fairly good (see WebGL support in different browsers).
Opera 12.16 has limited support for the W3C File API. In particular it does not support createObjectURL functionality, which means that it is not possible to use the browser's image codecs to decode preloaded files in the Emscripten virtual file system.
OpenAL and SDL audio support in Emscripten depend on the Web Audio API (see Web Audio API support in different browsers).